In order to test the Standard Model and search for new physics in experiments involving hadrons and nuclei, precision calculations of Standard Model observables are required.
To achieve this, Monte Carlo (MC) calculations of lattice-regularized path integrals for quantum chromodynamics (QCD) have been used to make precise predictions for many phenomenologically relevant quantities in the meson and nucleon sectors; for recent reviews see Refs. [1]}, [2]}, [3]}, [4]}, [5]}.
Lattice QCD calculations using MC methods are performed in Euclidean spacetime where the action \(S(U)\)  is typically a real function of the discretized gauge field \(U_{x,\mu } \in SU(3)\)  and an ensemble of gauge fields can be generated with probability distribution proportional to \(e^{-S(U)}\) .
Predictions for the expectation values of observables \(\mathcal {O}\)  are then obtained by averaging the results for \(\mathcal {O}(U)\)  obtained for each gauge field configuration.
